Řešení kvadratické rovnice v komplexních číslech
Řeš ve \( \C \) rovnici \( ix^2+\sqrt[4]{3}x-\frac{1}{4}=0 \)
\( \large\begin{aligned}K & =\left\{\frac{-\sqrt[4]{3}-\frac{1+\sqrt3}{2}-\frac{1-\sqrt3}{2}i}{2};\frac{-\sqrt[4]{3}+\frac{1+\sqrt3}{2}-\frac{1-\sqrt3}{2}i}{2}i\right.\\ & =\left\{\frac{1-\sqrt3}{4}+\frac{2\sqrt[4]{3}-1+\sqrt3}{4}i;\frac{-1+\sqrt3}{4}+\frac{2\sqrt[4]{3}+1-\sqrt3}{4}i\right\}\end{aligned} \)
\( \large\begin{aligned}K & =\left\{\frac{-\sqrt[4]{3}+\frac{1-\sqrt3}{2}-\frac{1+\sqrt3}{2}i}{2};\frac{-\sqrt[4]{3}-\frac{1-\sqrt3}{2}+\frac{1+\sqrt3}{2}i}{2}i\right.\\ & =\left\{\frac{1+\sqrt3}{4}-\frac{2\sqrt[4]{3}+1-\sqrt3}{4}i;\frac{-1-\sqrt3}{4}-\frac{2\sqrt[4]{3}-1+\sqrt3}{4}i\right\}\end{aligned} \)
\( \large\begin{aligned}K & =\left\{\frac{-\sqrt[4]{3}-\frac{1-\sqrt3}{2}+\frac{1+\sqrt3}{2}i}{2};\frac{-\sqrt[4]{3}+\frac{1-\sqrt3}{2}+\frac{1+\sqrt3}{2}i}{2}i\right.\\ & =\left\{\frac{1+\sqrt3}{4}+\frac{2\sqrt[4]{3}-1+\sqrt3}{4}i;\frac{-1-\sqrt3}{4}+\frac{2\sqrt[4]{3}+1-\sqrt3}{4}i\right\}\end{aligned} \)
\( \large\begin{aligned}K & =\left\{\frac{-\sqrt[4]{3}-\frac{1+\sqrt3}{2}-\frac{1-\sqrt3}{2}i}{2};\frac{-\sqrt[4]{3}+\frac{1+\sqrt3}{2}+\frac{1-\sqrt3}{2}i}{2}i\right.\\ & =\left\{\frac{1-\sqrt3}{4}+\frac{2\sqrt[4]{3}-1-\sqrt3}{4}i;\frac{-1+\sqrt3}{4}+\frac{2\sqrt[4]{3}+1+\sqrt3}{4}i\right\}\end{aligned} \)